International Journal of Tax Economics and Management Marginal Utility & its Diminishing Methods Luiz Carvalho Castro Department of Economic Sciences São Judas Tadeu University Email: [email protected] (Author of Correspondence) Antônio Souza Araujo Department of Economic Sciences São Judas Tadeu University Brazil Abstract In this article we have shown what is marginal utility in economics and its diminishing method mathematically. Marginal utility is an economic concept and very important to the theory of economic sciences. So we selected this topic to describe it with the concept of economics and mathematics elaborately. At the beginning of this article readers will find the definition of marginal utility and at the middle of this article, readers will find it's diminishing method mathematically. The term marginal utility has a good impact in economics. In economics, utility is the satisfaction or benefit derived by consuming a product; thus the marginal utility of a good or service is the change in the utility from an increase in the consumption of that good or service. Keywords: Marginal Utility; Diminishing Method; Marginality and Marxism; Theory of Marginal Utility. ISSN Online: 2618-1118 ISSN Print: 2618-110X 36 1. Introduction In the context of cardinal utility, economists sometimes speak of a law of diminishing marginal utility, meaning that the first unit of consumption of a good or service yields more utility than the second and subsequent units, with a continuing reduction for greater amounts. Therefore, the fall in marginal utility as consumption increases is known as diminishing marginal utility. 2. Marginality The term marginal refers to a small change, starting from some baseline level. As Philip Wicksteed explained the term, Marginal considerations are considerations which concern a slight increase or diminution of the stock of anything which we possess or are considering. Frequently the marginal change is assumed to start from the endowment, meaning the total resources available for consumption (see Budget constraint). This endowment is determined by many things including physical laws (which constrain how forms of energy and matter may be transformed), accidents of nature (which determine the presence of natural resources), and the outcomes of past decisions made by the individual himself or herself and by others. For reasons of tractability, it is often assumed in neoclassical analysis that goods and services are continuously divisible. Under this assumption, marginal concepts, including marginal utility, may be expressed in terms of differential calculus. Marginal utility can then be defined as the first derivative of total utility—the total satisfaction obtained from consumption of a good or service—with respect to the amount of consumption of that good or service. In practice the smallest relevant division may be quite large. Sometimes economic analysis concerns the marginal values associated with a change of one unit of a discrete good or service, such as a motor vehicle or a haircut. For a motor vehicle, the total number of motor vehicles produced is large enough for a continuous assumption to be reasonable: this may not be true for, say, an aircraft carrier. 3. Utility Depending on which theory of utility is used, the interpretation of marginal utility can be meaningful or not. Economists have commonly described utility as if it were quantifiable, that is, as if different levels of utility could be compared along a numerical scale. This has affected the development and reception of theories of marginal utility. Quantitative concepts of utility allow familiar arithmetic operations, and further assumptions of continuity and differentiability greatly increase tractability. Marginal Utility & its Diminishing Methods Contemporary mainstream economic theory frequently defers metaphysical questions, and merely notes or assumes that preference structures conforming to certain rules can be usefully proxied by associating goods, services, or their uses with quantities, and defines "utility" as such a quantification. Another conception is Benthamite philosophy, which equated usefulness with the production of pleasure and avoidance of pain, assumed subject to arithmetic operation. British economists, under the influence of this philosophy (especially by way of John Stuart Mill), viewed utility as "the feelings of pleasure and pain" and further as a "quantity of feeling". Though generally pursued outside of the mainstream methods, there are conceptions of utility that do not rely on quantification. For example, the Austrian school generally attributes value to the satisfaction of wants, and sometimes rejects even the possibility of quantification. It has been argued that the Austrian framework makes it possible to consider rational preferences that would otherwise be excluded. In any standard framework, the same object may have different marginal utilities for different people, reflecting different preferences or individual circumstances. 4. Diminishing Marginal Utility The concept in cardinal utility theory that marginal utilities diminish across the ranges relevant to decision- making is called the "law of diminishing marginal utility" (and is also known as Gosse n’s First Law). This refers to the increase in utility an individual gain from increasing their consumption of a particular good. "The law of diminishing marginal utility is at the heart of the explanation of numerous economic phenomena, including time preference and the value of goods ... The law says, first, that the marginal utility of each homogenous unit decreases as the supply of units’ increases (and vice versa); second, that the marginal utility of a larger-sized unit is greater than the marginal utility of a smaller-sized unit (and vice versa). The first law denotes the law of diminishing marginal utility; the second law denotes the law of increasing total utility." In modern economics, choice under conditions of certainty at a single point in time is modeled via ordinal utility, in which the numbers assigned to the utility of a particular circumstance of the individual have no meaning by themselves, but which of two alternative circumstances has higher utility is meaningful. With ordinal utility, a person's preferences have no unique marginal utility, and thus whether or not marginal utility is diminishing is not meaningful. In contrast, the concept of diminishing marginal utility is meaningful in the context of cardinal utility, which in modern economics is used in analyzing inter-temporal choice, choice under uncertainty, and social welfare. The law of diminishing marginal utility is similar to the law of diminishing returns which states that as the amount of one factor of production increases as all other factors of production are held the same, the marginal return (extra output gained by adding an extra unit) decreases. Copyright ©2019 | Seagull Publications 38 As the rate of commodity acquisition increases, marginal utility decreases. If commodity consumption continues to rise, marginal utility at some point may fall to zero, reaching maximum total utility. Further increase in consumption of units of commodities causes marginal utility to become negative; this signifies dissatisfaction. For example, Beyond some point, further doses of antibiotics would kill no pathogens at all, and might even become harmful to the body. To satiate thirst a person drinks water but beyond a point, consumption of more water might make the person vomit, hence leading to negative marginal and thus diminished total utility. It takes a certain amount of food energy to sustain a population, yet beyond a point, more calories cannot be consumed and are simply discarded (or cause disease). Diminishing marginal utility is traditionally a microeconomic concept and often holds for an individual, although the marginal utility of a good or service might be increasing as well. For example: I. bed sheets, which up to some number may only provide warmth, but after that point may be useful to allow one to effect an escape by being tied together into a rope; II. tickets, for travel or theatre, where a second ticket might allow one to take a date on an otherwise uninteresting outing; III. Dosages of antibiotics, where having too few pills would leave bacteria with greater resistance, but a full supply could effect a cure. IV. The third leg is more useful than the first two when building a chair. As suggested elsewhere in this article, occasionally one may come across a situation in which marginal utility increases even at a macroeconomic level. For example, the provision of a service may only be viable if it accessible to most or all of the population, and the marginal utility of a raw material required to provide such a service will increase at the "tipping point" at which this occurs. This is similar to the position with very large items such as aircraft carriers: the numbers of these items involved are so small that marginal utility is no longer a helpful concept, as there is merely a simple "yes" or "no" decision. 5. Marginality Theory Marginalize explains choice with the hypothesis that people decide whether to effect any given change based on the marginal utility of that change, with rival alternatives being chosen based upon which has the greatest marginal utility. Marginal Utility & its Diminishing Methods 6. Market Price and Diminishing Marginal Utility If an individual possesses a good or service whose marginal utility to him is less than that of some